From among all of the problem solving strategies that children can use, how do they decide which ones to use? Illustratively, when children spell a word, sometimes they retrieve a spelling and write it, other times they sound out a spelling phonetically, still other times they look up the word in a dictionary. Even preschoolers appear quite adept at making adaptive strategy choices, that is, at making choices that meet the twin goals of accuracy and efficiency. The goals of the present research project are to specify how children decide which strategy to use, how the ability to make such choices develops, and what functions the strategy choice process serves. A variety of methodologies will be used to pursue these goals. The basic one will involve making videocassettes of children's performance, and examining their audible and visible behaviors between presentation of the problem and statement of the answer. The videocassettes will help in identifying what strategies children are using, how long each strategy takes to execute, and how accurate it is. Supplementing these empirical techniques will be two types of formal modeling: mathematical modeling of the strategy choice process, and computer simulation of the way in which the process develops. The proposal involves the extension of work already conducted in addition and subtraction to three other domains of daily importance in children's lives: spelling, reading, and multiplication. Also proposed are experiments aimed at deepening our understanding of strategy choices in addition and subtraction. Several quite applied problems will be examined within these domains, such as the wisdom of teachers instructing children not to use their fingers to add and subtract. The goal is to obtain both broad and deep understanding of the development of strategy choice procedures.